# "Geometry of 2-dimensional spheres"

## Dr. Regina Rotman, University of Toronto

### Wednesday, March 13, 2013

3:40–5 p.m.

Location: Surge Building 284

Parking Information

Category: Colloquium

Description: Tea time @ 3:40 p.m.

Talk begins @ 4:10 p.m.

Ends @ 5:00 p.m.

Abstract:

I will discuss some geometric inequalities that are valid for Riemannian manifolds diffeomorphic to the sphere of dimension 2.

For example, consider the following basic question: Suppose a simple closed curve $\gamma$ on a Riemannian sphere M of diameter D can be contracted to a point in M over simple closed curves of length at most L. Is there a homotopy over loops based at some point of $\gamma$ that are short compared to L and D? The answer to this question is positive. (Joint with G. Chambers.)

I will also prove that for any positive k and any two points of M there exist at least k geodesics connecting them of length at most 22kD. (Joint with A. Nabutovsky.)

Additional Information: Math Colloquiums

Open to: General Public

Admission: Free

Sponsor: Mathematics

Contact Information:

Dr. Fred Wilhelm

wilhelm@math.ucr.edu